Question

A thermally insulated chamber or volume $2V_0$ is divided by a frictionless piston of area $S$ into tan goal parts $A$ and $B$ . Part $A$ has an ideal gas at pressure $P_0$ and temperature $V_0$ and in part $B$ vacuum. A massless spring of force constant $k$ is connected with piston and the wall of the container as shown. Initially spring is unstretched. Gas in chamber $A$ is allowed to expand. Let in equilibrium spring is compressed by $x_0$ . Then:

• A. Final pressure of gas is $\frac{k{x}_{0}6}{S}$
• B. Work done by the gas is $\frac{1}{2}k{x}_0^2$
• C. Change in internal the gas is $\frac{1}{2}k{x}_0^2$
• D. Temperature of the gas is decreased.

Answer 1

The correct option is B Work done by the gas is $\frac{1}{2}k{x}_0^2$

In this case work done by the gas is equal to potential energy stored in the spring.

$W=\frac{1}{2}k{x_0}^2$